These suggestions will be based on timing and assumptions.
If you arrive from Manchester on time ( I’m assuming you are arriving by train at Euston station) it will be another 30-60 minutes before you get settled at the Hyatt. Lets say you’ll be ready to head out from the hotel by 2pm.
As you mentioned bicycles I suspect you are fit and don’t mind walking, which, to me is the best way to see London.
Thoughts:
See a few of the iconic sites exterior POV only. I’m referring to Buckingham Palace, Parliament and Westminster Abbey known as Parliament Square. From the Hyatt Its a 2 mile stroll from to there. If your timing is close Big Ben, the bell inside Elizabeth’s Tower will chime on the hour. That occurrence will establish you are not in Kansas anymore. From Parliament Square follow Birdcage Walk up to the Palace. Then head through Green Park to the Rose and Crown pub for a pint and some food. Then you could walk in Hyde Park towards Marble Arch and back to the Hyatt.
Another option is see Parliament Square then walk over Westminster Bridge and follow the Thames path by the London Eye past Jubilee Gardens. Past the carousel is Beany Green where you can grab a coffee. Little booth at the foot of the Jubilee Bridge.
The view back towards Parliament is the iconic POV.
Really nice at sunset. From here stroll up to see the graffiti tunnel near Waterloo station.
A third idea would be from the Hyatt walk to Bond Street Underground Station and board Jubilee Train (gray ) to Baker Street Station, Mind the Gap and board a Bakerloo train ( brown) to Warwick Ave. Exit the station and walk a long block to the Regent Canal and follow the canal path.
I’m referencing colors because on the tube map you’ll see each line has a designated color.
If you can find them the pocket size tube maps are great.
London is never boring. Lots to explore and experience even in a short amount of time.